Remote material identification process performance prediction tool

ABSTRACT

In accordance with the present disclosure, a computer implemented system and method predicts the performance for a remote material identification process under real conditions and uncertainties. The method and system transforms data representing measured reflectance values for candidate materials based on environmental conditions, and uncertainties regarding the environmental conditions and/or calibration of sensors measuring radiance values into the performance predictions for a material identification process operating under those conditions and uncertainties. The performance predictions can be communicated to a designer of, for example, a multi-angle material identification system for use in selecting and setting up the system, or communicated to a consumer of images captured by the material identification system for use in interpreting results of application of the material identification process to real imagery acquired with remote sensors.

The U.S. government may have certain rights in this invention pursuantto its funding under contract No. 2004-K724300-000.

FIELD

The present disclosure generally relates to material identificationprocesses, and relates in particular to a performance prediction toolfor such processes.

BACKGROUND

Material identification using a remotely located sensor is used for anumber of purposes, for example detection, identification andclassification of objects within a scene, and applications, forcharacterization of urban areas, search and rescue, differentiatingcombatant forces, and detection of attempts at camouflage, denial anddeception. It is based on the general principle that the observedspectral radiance of any given target will vary based on, among otherthings, the type of the material of which the surface of the target ismade. Different materials absorb, reflect and emit differently,depending on wavelength. The spectral radiance of a target—the surfaceof a particular object within a scene—from a given angle or directioncan be measured using various types of sensors, depending on thewavelengths of interest. Based on the measured or observed spectralradiance it is possible to determine the material of which the surfaceis made.

Several types of remote sensors and imaging modalities have been used togenerate image sets containing both spectral and spatial information ofreal scenes for purposes of detection, identification or classificationof objects within the scene. Electro-optical sensors are typicallysingle band, multispectral or hyperspectral. A multispectral sensordetects and records radiation in a limited number of bands that aretypically fairly wide, for example in the red, blue, green, andnear-infrared bands of the spectrum. A hyperspectral sensor detectsradiation in a large number of contiguous bands, typically throughoutthe visible and near-infrared regions of the spectrum. Other types ofimaging modalities, for example, synthetic aperture radar (SAR),typically operate only in a single band. The sensors are typically (butdo not have to be) placed in satellites or aircraft and acquire imagesof portions of the surface of the earth during flyovers at relativelyhigh altitudes. However, it is possible for the sensors to be placed onthe ground.

Each “image”—also called “imagery” or “image set”—of a scene generatedby such a sensor comprises spatial information, typically in twodimensions. It also contains spectral radiance information, which wouldinclude the radiance of at least one predetermined band of wavelengthsthat the sensor can detect. The material of which at least the surfaceof an object within the scene is made—the “target”—is identified byselecting within the image the pixels comprising the target andevaluating the spectral radiance to develop a spectral signature forthat target that can be compared to known spectral signatures of variousmaterials. In automatic material identification a specially programmedcomputer is used to process image data from a remote sensor and otherdata to identify the material of the target.

The spectral radiance—radiance at a given wavelength or band—for anygiven target in a scene will depend on the material of which the targetis composed (the “target material”), as well as the spectrum and angleof irradiation being reflected by the target, the atmospheric conditionsthrough which both the illuminating irradiation and the reflectedradiation travels, and the spectrum of any emitted radiation. In orderto make the identification, measured spectral radiance is typicallytransformed to an estimated reflectance. Reflectance is the ratio of themeasured radiance from an object divided by the radiance reflected by a100% Lambertian reflector. When using images of real targets,reflectances are estimated by taking into account relevant environmentalconditions, such as the radiation source and atmosphere, under which theimagery was acquired.

The way in which a surface reflects or emits radiation can be generallycategorized as either Lambertian or non-Lambertian. A Lambertian surfacescatters electromagnetic radiation equally in all directions, withoutregard to the direction of illumination. Thus, its reflectance isgenerally isotropic or the same in all directions. A non-Lambertiansurface does not scatter incident electromagnetic radiation equally inall directions. Examples of non-Lambertian surfaces include those thatare backscattering, meaning that the light scatters predominantly towardthe illumination source; forward scattering, meaning scatteringpredominantly in directions away from the illumination source; andspecular, meaning reflecting the illumination source like a mirror. Manyman-made objects or targets exhibit non-Lambertian reflectance.

SUMMARY

In accordance with the present disclosure, a computer implemented systemand method predicts the performance for a remote material identificationprocess under real conditions and uncertainties. The method and systemtransforms data representing measured reflectance values for candidatematerials based on environmental conditions, and uncertainties regardingthe environmental conditions and/or calibration of sensors measuringradiance values into the performance predictions for a materialidentification process operating under those conditions anduncertainties. The performance predictions can be communicated to adesigner of a material identification system for use in selecting andsetting up the system, or communicated to a consumer of images capturedby the material identification system for use in interpreting results ofapplication of the material identification process to real imageryacquired with remote sensors.

To identify a material within an image, the remote materialidentification process may be treated as Lambertian, meaning that itsspectral signature does not change with illumination or viewinggeometry, or non-Lambertian. If the materials are processed to beLambertian, the directional hemispherical reflectance (DHR) for eachcandidate material, which relates, for a given wavelength or band ofwavelengths and direction of incident irradiation, reflected radianceacross the entire hemisphere, is used to predict the spectralreflectance of the candidate material. The target may also be treated asnon-Lambertian, meaning that its spectral signature changes withillumination and viewing geometry. The candidate materials are alsotreated as non-Lambertian. The bi-directional reflectance distributionfunction (BRDF) for each candidate material, which relates, for a givenwavelength or band of wavelengths and direction of incident irradiation,reflected radiance in the direction of the sensor, is used to predictthe spectral reflectance of the candidate material.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a conceptual block diagram illustrating a computerizedapparatus for predicting the performance of a remote sensor materialidentification process under one or more environmental conditions anduncertainties.

FIG. 2 is a system block diagram illustrating a computer implementedsystem for predicting the performance of a remote sensor materialidentification process under one or more environmental conditions anduncertainties.

FIG. 3 is a flow diagram illustrating a computer implemented method forpredicting the performance of a remote sensor material identificationprocess under one or more environmental conditions and uncertainties.

FIG. 4 is a system block diagram illustrating a computer implementedsystem for simulating a “true” multi-angle target signature for anon-polarimetric reflective and/or emissive, multi-spectral (MS),multi-angle material identification process.

FIG. 5 is a graphical representation illustrating an example ofperformance predictions for a multi-angle material identificationprocess.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

In the following description, like numbers refer to like elements.

Referring to FIG. 1, a performance prediction tool (PPT) 100 is oneexample of a system performing a method for quantifying performance of aremote identification process based on real environmental conditions anduncertainties associated with measurements and other aspects of thematerial identification process. The material identification processprovides a method for identifying target materials by comparing theirspectral signatures to candidate spectral signatures estimated using adatabase of bi-directional reflectance distribution function (BRDF)measurements of materials. The BRDFs are based, at least in part, onspectral measurements taken of actual materials. One example of a BRDFdatabase is the Nonconventional Exploitation Factor (NEF) database.NEFDS is a set of software programs for use in obtaining information fora given material from the NEF database. Described in a patentapplication, entitled “Remote Identification of Non-LambertianMaterials,” filed concurrently herewith, and naming Joseph C. Landry,Paul M. Ingram, John J. Coogan and Paul D. Shocklee as inventors, is adescription of a material identification process for non-Lambertianmaterials that utilize a multi-angle spectral signature for materialidentification. The disclosure of the aforementioned patent applicationis incorporated herein in its entirety for any and all purposes.

The PPT 100 is comprised of, in one embodiment, a specially programmedcomputer. The computer is comprised of one or more processors forexecuting programmed instructions stored in a memory or other computerreadable medium. The instruction causes the computer to perform thesteps of the processes described below. The PPT 100 is further comprisedof, or has access to, the BRDF database 102. The BRDF database may belocal or remote. The PPT 100 quantifies the performance as a function ofthe sensor system and environmental parameters and their uncertainties.These environmental parameters and uncertainties are given valuesprovided to a computer processor 104 of the PPT 100 via a user inputdevice 106 connected to the computer processor 104, such as a keyboard,mouse, or other input device or network link to such a device. Thecomputer processor 104 can provide this performance information to auser by a user output device 108 connected to the computer processor,such as a dynamic display, printer, or other local device connected tothe computer by a local interface or network link. This information canbe provided, for example, to a system designer to set requirements onsystem parameters such as sensor radiometric and spectral calibrationuncertainty and aerosol parameter uncertainty. It can alternatively oradditionally be provided to a user of the remote material identificationprocess as an aid in deciding how much confidence to attribute to anidentification.

Performance of a material identification process is expressed in termsof two kinds of mistakes that can occur during a material identificationprocess. The first kind of mistake occurs when the correct candidatematerial is declared not to match the target (a missed detection or“miss”). These mistakes are characterized by the probability ofdetection P_(d), which is actually the probability of the complementaryevent, i.e. of a “hit”. The second kind of mistake occurs when anincorrect candidate material is declared to match the target (a falsealarm). These mistakes are characterized by the probability of falsealarms P_(fa). Performance is expressed as the P_(fa) associated with agiven P_(d). Paired (P_(d), P_(fa)) values can be used to constructreceiver-operator characteristic (ROC) curves for describing theperformance of hypothesis tests like the one used in the PPT 100. Such acurve can be displayed or otherwise communicated to a user via useroutput device 108 (FIG. 1). Paired (P_(d), P_(fa)) values can also beused to construct curves, like the ones graphically represented in FIG.5, discussed below, to characterize the number of incorrectly matchedmaterials for a given value of P_(d) and given levels of uncertainty invarious input parameters. Alternatively, the information can becommunicated in the form of a table like Table 5, discussed below.

The PPT can allow the user to determine P_(fa) values for a given valueof P_(d), or vice versa, as a function of one or more system andenvironmental parameters, and thus to quantify changes in performancewith changing system requirements, scene content and environmentalknowledge. Examples of such system and environmental parameters are:

-   -   Acquisition geometry (sun and sensor angles) of each image    -   Target and background materials present in the scenes    -   Atmospheric conditions and uncertainties    -   Sensor radiometric and spectral calibration parameters and        uncertainties    -   Candidate material BRDF measurements and uncertainties    -   Orientation of the surface normal of the target and        uncertainties

The PPT can be employed with various imaging modalities as follows:

-   -   Non-polarimetric reflective and/or emissive, multi-spectral (MS)        or hyperspectral (HS)    -   Polarimetric spectral reflective and/or emissive, MS or HS    -   Synthetic aperture radar (SAR) and other active sensing        modalities

The components in an example of a PPT 100 are described with referenceto FIG. 2, while a generalized example of a PPT method is described withreference to FIG. 3. FIG. 4 and related discussion provide a fulldescription of one example of a process performed by the PPT 100 for amaterial identification process using non-polarimetric (non-PI)reflective MS imagery. FIG. 5 and Tables 1-5 give three exampleapplications of the PPT to non-PI reflective MS imagery, showing how itcharacterizes the performance of the algorithm.

Referring to FIG. 2, the performance prediction process carried out by,for example, the PPT process and system is organized into three primarycomponents that accomplish the performance predictor tool. First,simulation component 200 takes as input atmospheric parameters 202provided by a user, and background and target data 204 from a BRDFdatabase 206, including background parameters and target parameters, allof which are taken to be “true.” Simulation component 200 utilizes thisinput to generate at least one target signature 208 by simulating aground truth imagery collection campaign of known targets andbackgrounds by modeling the target and background radiance signatures.The simulated “true” target and background radiance signatures aredetermined for a given imaging modality from a given angle. Truesignature radiances for more than one angle can be simulated. Then amaterial identification process 210 is executed with “true” targetsignature 208 and “true” atmospheric parameters 202, with additionalinput 212 to generate the results for the material identificationprocess. The additional input 212 includes candidate signatureparameters and uncertainty for the target material and each candidatematerial used in the material identification process. The additionalinput 212 also includes uncertainties that can be specified by a systemuser, such as given measurement uncertainties for atmospheric parametersand signature measurement, and a given probability of detection P_(d).Finally, a performance assessment component 214 uses these results tocalculate the probability of a false alarm (P_(fa)) 216 associated witha given candidate material.

Turning to FIG. 3, the illustrated computer-implemented performanceprediction method transforms specific information regarding measuredmaterial reflectance information from a BRDF database into performancepredictions. These performance predictions predict performance of aremote material identification process being used to identify thematerial of which real targets are made using imagery processed from oneor more remote sensors. The performance predictions are communicated todesigners and users of the remote material identification process,and/or consumers of imagery analyses carried out according to the remotematerial identification process. The computer-implemented method can beused to predict the performance of a remote sensor materialidentification process using real imagery under different conditions—forexample, different target materials, different backgrounds, differentsensors, different acquisition angles, different imaging modalities, anddifferent characteristic conditions—and uncertainties, such asuncertainties arising from characterization of atmospheric conditions,with calibration of imagery sensors (both power and spectral), and BRDFparameters.

Beginning at step 218, the method initially sets one or moreenvironmental parameters representative of the one or more environmentalconditions and one or more uncertainties. The uncertainties set by thecomputer at step 218 can be associated with, for example, theenvironmental parameter or parameters, or calibration of the remotesensor or sensors that will be used in the acquisition of real imagery.A user may specify to the process the environmental parameters, theenvironmental conditions, and the uncertainties. Step 218 can alsoinclude receiving from a user a probability of detection value andsetting a probability of detection variable to the received value.

At step 220, the computer-implemented method simulates a “true” targetradiance signature that would be acquired by a sensor under “true”environmental conditions. The spectral radiance for one or more bandsfor a preselected target material and background, are determined using aprocess illustrated by FIG. 4. These “true” radiances in preselectedenvironmental conditions, substitute for the measured radiance of theselected target material in imagery acquired using the one or moresensors, and are then used as input to the remote materialidentification process, the performance of which is to be predictedunder the preselected environmental conditions, but with uncertaintiesassociated with real world measurement of the environmental conditionsand the target radiance, and with the material identification processbeing tested.

Once the “true” target radiance signature has been simulated at step220, the method uses this simulated “true” target radiance signature atstep 222 to perform a remote material identification process. In theexamples given herein, the target signature is comprised of the spectralsignature of the target in one or more wavelength bands from one or moreacquisition angles. In the material identification process of step 222,this “true” spectral radiance signature for the target substitutes forthe spectral radiance of the target obtained from imagery of realterrain containing the target. The remote material identificationprocess carried out in step 222 also utilizes the one or more “true”environmental parameters which were used to simulate the “true” radiancesignature of the target, and the uncertainties associated with theseparameters that would be present in the real world measurements orknowledge of the environmental conditions (e.g., atmospheric parameteruncertainty). The process carried out in step 222 further uses radiancemeasurement uncertainty (e.g., the sensor calibration), BRDF parametersfor candidate materials used in the identification process, anduncertainties associated with these parameters. The remote materialidentification process is then executed to identify at least one of thecandidate materials of which the target is made. It is assumed that thematerial identification process utilizes the chi-square test, so step222 can include utilizing a probability of detection given by the userof the PPT for the material identification process in order to generatethe results of the material identification process.

Once the material identification process of step 222 has been completed,the results of that process can be employed at step 224 to determine aprobability of a false identification. These results can be recorded atstep 226 in a computer readable medium. An environmental parameter or anuncertainty can be varied or changed, as indicated by steps 228 and 230,and the process repeated for step 218. Similarly, the process can berepeated for a different target material, as indicated by steps 232 and234. The results for all of the conditions, uncertainties, and targetmaterials tested can be communicated to a user or to another program atstep 236.

Turning now to FIG. 4, illustrated is an example of a process fordetermining the background and target radiances. This example isparticularly described as it applies to non-polarimetric reflectivemulti-spectral imagery. Substantially similar processes can be used forother imaging modalities.

Aerosol properties 238 are characterized by the spectral extinctionε_(λ), absorption α_(λ) and asymmetry ψ_(λ) parameters, where λ denoteswavelength. The background and target radiance spectra imaged atmultiple acquisition geometries in the same pass can be simulated. Forthis example, it is assumed that the atmospheric conditions along thelines of sight are identical for all images, and only the acquisitionangles change.

Assuming that the true aerosol spectral parameters ε=ε_(λ), α=α_(λ), andψ=ψ_(λ), and other atmospheric parameters are given, two sets ofatmospheric correction terms are calculated, one in each branch of theFigure. In the left branch, a first simulation component 240 determinesthe spectral background-independent path terms (BIP) 242 from aerosolproperties 238, including ε, α, ψ, and other environmental parameters. Asecond simulation component 244 converts these BIP 242 intobackground-dependent path terms (BDP) 246 using the directionalhemispherical spectral reflectance 248, denoted ρ_(λ) ^(b), of theLambertian background as a function of wavelength λ obtained from a BRDFdatabase, which in this example is the NEF database 250, using apreselected background same as might be encountered in actual imagery.In the right branch, a third simulation component 252 determines the NEFatmospheric transmittance and downwelling radiance terms (ATM) 254 fromthe aerosol properties 238, including ε, α, ψ, and from ρ_(λ) ^(b) 248from the NEF database. The NEF atmospheric terms are, in this example,calculated assuming that the target is horizontal. A fourth simulationcomponent 256 passes the ATM 254 data to the NEF database 250, where thefollowing aperture effective values (AEV) 258 are computed and returned:

-   -   ρ_(D) ^(b): the directional hemispherical reflectance of the        background    -   ρ_(D) ^(t): the directional hemispherical reflectance of the        target    -   ρ_(SL) ^(b): the Lambertian-equivalent solar reflectance of the        background    -   ρ_(SL) ^(t): the Lambertian-equivalent solar reflectance of the        target

Finally, a fifth simulation component 260 determines background andtarget radiances 262 using the BDP 246 and the AEV 258. For example, theaperture radiance of the background L^(b) is determined from BDP 246,ρ_(D) ^(b) and ρ_(SL) ^(b), and the aperture radiance of the target iscalculated from BDP 246, ρ_(D) ^(t) and ρ_(SL) ^(t). The steps in thePPT process are summarized in equation (1.1):

$\begin{matrix}{{ɛ_{\lambda},\alpha_{\lambda},\left. \psi_{\lambda}\rightarrow{{BIP}\overset{\rho_{\lambda}^{b}}{\rightarrow}{BDP}} \right.}{ɛ_{\lambda},\alpha_{\lambda},\psi_{\lambda},\left. \rho_{\lambda}^{b}\rightarrow{{ATM}\overset{NEF}{\rightarrow}\rho_{D}^{b}} \right.,\rho_{SL}^{b},\rho_{D}^{b},{\rho_{SL}^{b}\overset{BDP}{\rightarrow}L^{b}},L^{t}}} & (1.1)\end{matrix}$

These operations are described below.

The spectral BIP terms 242 appropriate for the reflective region can bemade up of the following quantities indexed by wavenumber v. Thesequantities can be determined, for example, as functions of aerosolproperties and acquisition geometry using the software program calledMODTRAN®, which is a program owned by the U.S. Air Force ResearchLaboratory, maintained by Spectral Sciences Inc. and distributed byOntar Corporation:

-   -   L_(v) ^(AS)—Solar photons that are scattered into the sensor's        field of view via single or multiple scatter events within the        atmosphere without ever reaching the target or background.    -   L_(v) ^(DSR)—Solar photons that pass directly through the        atmosphere to a 100% reflectance Lambertian target, reflect off        the target, and propagate directly through the atmosphere to the        sensor. Light for this path term is attenuated by absorption and        by light scattering out of the path, but no radiance is        scattered into the path. This path does not involve any        interaction with the background.    -   L_(v) ^(SSR)—Solar photons that are scattered by the atmosphere        onto a 100% reflectance Lambertian target, reflect off the        target, and propagate directly through the atmosphere to the        sensor. This path term does not involve any interactions with        the background.    -   L_(v) ^(BDSR)—Solar photons that are directly transmitted to a        100% reflectance Lambertian background, reflect off the        background once, and then scatter into the field of view of the        sensor.    -   L_(v) ^(BSSR)—Solar photons that are scattered by the atmosphere        at least once, reflect off a 100% reflectance Lambertian        background once, and then scatter into the field of view of the        sensor.    -   S_(v)—Spherical albedo of the bottom of the atmosphere, which        can be thought of as a reflection coefficient of the atmosphere.

The MODTRAN® program can be executed as a separate process on the samecomputer as the PPT 100 or on a different computer.

The spectral BIP terms 242 can be used to calculate the spectral targetradiance L_(v) as shown in equation (1.2), where ρ_(v) ^(t) is the NEFAEV of the target spectral reflectance and ρ_(v) ^(b) is the AEV of thebackground spectral reflectance.

$\begin{matrix}\begin{matrix}{L_{v} = {{\rho_{v}^{SL}L_{v}^{DSR}} +}} & {\mspace{14mu} \begin{matrix}{\ldots \mspace{14mu} {target}\mspace{14mu} {reflected}\mspace{14mu} {direct}} \\{{solar}\mspace{14mu} {radiance}}\end{matrix}} \\{{\frac{\rho_{v}^{D}}{1 - {\rho_{v}^{b}S_{v}}}\left( {{\rho_{v}^{b}S_{v}L_{v}^{DSR}} + L_{v}^{SSR}} \right)} +} & {\mspace{11mu} \begin{matrix}{\ldots \mspace{14mu} {target}\mspace{14mu} {reflected}\mspace{14mu} {scattered}} \\{d{ownwell}}\end{matrix}} \\{L_{v}^{AS} + {\frac{\rho_{v}^{b}}{1 - {\rho_{v}^{b}S_{v}}}\left( {L_{v}^{BDSR} + L_{v}^{BSSR}} \right)}} & {\; \begin{matrix}{{{\ldots \mspace{14mu} {atmospheric}}\&}\mspace{14mu} {background}} \\{scatter}\end{matrix}}\end{matrix} & (1.2)\end{matrix}$

The NEF database 250 provides the spectral reflectance 248, denotedρ_(λ) ^(b) of the selected background. Then ρ_(λ) ^(b) is converted toρ_(v) ^(b), where v denotes wavenumber. Next, ρ_(v) ^(b), and the sensorspectral response R_(i)(v) are spectrally resampled to the uniformlyspaced wavenumber samples in the spectral BIP terms 242. Finally, thetrue band-integrated BDP terms 246 can be determined as shown inequation (1.3) via the extended trapezoidal rule:

$\begin{matrix}{{L_{i}^{TRDS} = {\int{L_{v}^{DSR}{R_{i}(v)}{v}}}}{L_{i}^{TRH} = {\int{\frac{1}{1 - {\rho_{v}^{b}S_{v}}}\left( {{\rho_{v}^{b}S_{v}L_{v}^{DSR}} + L_{v}^{SSR}} \right){R_{i}(v)}{v}}}}{L_{i}^{PSMS} = {\int{\left\lbrack {L_{v}^{AS} + {\frac{\rho_{v}^{b}}{1 - {\rho_{v}^{b}S_{v}}}\left( {L_{v}^{BDSR} + L_{v}^{BSSR}} \right)}} \right\rbrack {R_{i}(v)}{v}}}}} & (1.3)\end{matrix}$

The directional hemispherical spectral reflectance ρ_(λ) ^(b) of theLambertian background is used to create a MODTRAN “spec_alb.dat” file.This file and the aerosol parameters 238, including ε, α and ψ, are usedto calculate the NEF atmospheric transmittance and downwelling radianceterms ATM 254, which can be made up of the following quantities. Thesecan be determined as functions of wavelength λ, zenith angle θ_(i) andazimuth angle φ_(i):

-   -   τ(λ, θ_(i))—transmittance from target to sensor along a line of        sight with zenith angle θ_(i).    -   L(λ, θ_(i), φ_(i))—radiance incident on the target from        direction (θ_(i), φ_(i)).

The true band-integrated background radiance L_(i) ^(b) in band i can beobtained by integrating equation (1.2) with respect to R_(i)(v) whenρ_(v) ^(t)=ρ_(v) ^(b) to obtain equation (1.4):

$\begin{matrix}{L_{i}^{b} = {\int{\left\lbrack {L_{v}^{AS} + {\frac{\rho_{v}^{b}}{1 - {\rho_{v}^{b}S_{v}}}\left( {L_{v}^{DSR} + L_{v}^{SSR} + L_{v}^{BDSR} + L_{v}^{BSSR}} \right)}} \right\rbrack {R_{i}(v)}{v}}}} & (1.4)\end{matrix}$

Alternatively, L_(i) ^(b) can be evaluated by substituting ρ_(i)^(SL)=ρ_(i) ^(D)=ρ_(i) ^(b) into equation (1.5), where ρ_(i) ^(b) is theNEF band-integrated AEV value of the background reflectance.

The NEF database 250 is used to calculate the band-integrated AEVs ofthe target directional hemispherical reflectance ρ_(i) ^(D) and targetLambertian-equivalent solar reflectance ρ_(i) ^(SL) in each band i. Ifit is assumed that the target is horizontal, then the trueband-effective target radiance in band i is given by equation (1.5):

L _(i) ^(t)=ρ_(i) ^(SL) L _(i) ^(TRDS)+ρ_(i) ^(D) L _(i) ^(TRH) +L _(i)^(PSMS)  (1.5)

A material identification method is next executed with the targetradiance spectra L^(t) simulated for N_(images) acquisition geometries.It can be assumed that the estimated aerosol spectral parameters{circumflex over (ε)}={circumflex over (ε)}_(λ)={circumflex over(α)}={circumflex over (α)}_(λ) and {circumflex over (ψ)}={circumflexover (ψ)}₂ have already been obtained from some source.

The material identification method can assume that errors in each of theN_(bands) component of each measured target radiance spectrum arezero-mean Gaussian random variables with standard deviations that areproportional to the radiance value by a factor σ_(cal) which can be setby the user. It can also be assumed that these errors are independentband-to-band and image-to-image. The process can be easily modified toaccommodate errors that are correlated band-to-band and image-to-imageif such correlation coefficients are available.

The material identification method can also assume that errors in themeasured aerosol parameters are zero-mean Gaussian random variables withknown standard deviations that are proportional to the parameter valueby factors σ_(δε), σ_(δα) and σ_(δψ) which can be set by the user. Itcan also be assumed that these errors are independentparameter-to-parameter and band-to-band. The process can be easilymodified to accommodate errors that are correlatedparameter-to-parameter and band-to-band if such correlation coefficientsare available.

The material identification method calculates an uncertainty in thecandidate signatures attributable to NEF BRDF measurement errors basedon the error covariance matrix supplied by the NEF database 250.

When a correct candidate is chosen, the expected value of the targetreflectance signature {circumflex over (ρ)}^(t) and the candidatereflectance signature {circumflex over (ρ)}^(c) will be equal and theexpected value of the difference signature is ξ=0. In this case, the χ²statistic should have a chi-square distribution with number of degreesof freedom v=N_(bands)·N_(images). Denote the inverse cumulativedistribution function by Q_(χ) ₂ . For a given probability of detectionP_(d), a chi-square threshold x is set as shown in equation (1.6):

x=Q _(χ) ₂ (P _(d) ,v)  (1.6)

When the incorrect candidate is chosen, the expected values of{circumflex over (ρ)}^(t) and {circumflex over (ρ)}^(c) will typicallydiffer. In this case the χ² statistic should have a non-centralchi-square distribution with the same number of degrees of freedomv=N_(bands)·N_(images) as for the correct candidate, and withnon-central parameter λ=χ². Denote the cumulative distribution functionby P_(nc-) _(χ) ₂. Then the probability of false alarms P_(fa) iscalculated from the threshold x in accordance with equation (1.7):

P _(fa) =P _(nc-) _(χ) ₂(x,v,λ)  (1.7)

Three example applications for the performance prediction apparatus,system, and method described above illustrate how it characterizes theperformance of the material identification method. In this particularexample, each of the tests was executed for a desert scenario defined bythe following parameters:

TABLE 1 Parameter Value Sensor Ikonos blue, green, red and NIR bandsAERONET aerosol type Desert Dust Visibility 11 km Sun elevation 45°Sensor elevation 45° Relative azimuths 95° and 175° NEF version 12.1.2.6NEF background natural-surface~soil~arid~playa

The application described below illustrates the predicted performance ofa remote material identification process utilizing spectral signaturesof the same target acquired at or near specular geometry and the otherat off specular geometry. Here, in this example, the PPT is used tosimulate a ground truth collection for a target consisting of NEFmaterial 0835UUUPNT, described as “silver-gray weathered paint chip(over tarpaper)”. Additional parameters involved in the ground truthsimulation are listed in Table 1. The sensor calibration uncertainty istaken to be 4% and the aerosol parameter uncertainty is taken to be 10%.

Execution of the PPT for these conditions determines the P_(fa) valuesfor each candidate NEF material corresponding to a P_(d) value of 95%.The P_(fa) is calculated for the target signature from each imageseparately and for the combined target signature. The results are shownin Tables 2.

Table 2 shows the three resulting P_(fa) values for each NEF material,sorted by off-specular P_(fa) value in decreasing order. The secondcolumn of this table shows that if only the off-specular image wereavailable, the target would be confused with many incorrect candidatematerials. When the near-specular image is also available, the P_(fa)values in the second column drop to the values in the last column. Thenear-specular signature significantly suppresses false alarms for thelisted NEF candidates.

TABLE 2 P_(fa) for off- P_(fa) for near- P_(fa) for Candidate specularspecular combined Material signature signature signature 0724UUUPNT0.9341 0.012 0.0307 0122UUUALM 0.91 0 0 0400UUUCNC 0.8926 0 0 1004UUUCNC0.8766 0.0087 0.0203 0603UUUCNC 0.8459 0 0 1312UUUALM 0.807 0 00898UUUFAB 0.6951 0 0 0971UUUCNC 0.6559 0 0 0893UUUFAB 0.5378 0 00588UUUCNC 0.5236 0 0 0605UUUSTO 0.5217 0 0 0838UUUPNT 0.5033 0 00713UUUCNC 0.4898 0 0 0014UUUALM 0.3983 0 0 0899UUUFAB 0.394 0 00671UUUCNC 0.3692 0 0 0593UUUCNC 0.2787 0 0 1074UUUFABa 0.2585 0 01039UUUCNC 0.2442 0 0 0864UUUCNC 0.2141 0 0 0822UUUPNT 0.2139 0 00490UUUASP 0.2083 0 0 0677UUUCNC 0.1892 0 0 0920UUUGRV 0.1613 0 00892UUUFAB 0.143 0 0 0915UUUCNC 0.132 0 0 0420UUUSTL 0.0623 0 00919UUUCNC 0.0607 0 0 1040UUUCNC 0.0563 0 0 0746UUUPNT 0.0445 0 0

Table 3 shows the three resulting P_(fa) values for each NEF material,sorted by near-specular P_(fa) value in decreasing order. The thirdcolumn of this table shows that if only the near-specular image wereavailable, the target would be confused with many incorrect candidatematerials. When the off-specular image is also available, the P_(fa)values in the third column drop to the values in the last column. Theoff-specular signature significantly suppresses false alarms for thelisted NEF candidates.

TABLE 3 P_(fa) for off- P_(fa) for near- P_(fa) for Candidate specularspecular combined Material signature signature signature 0906UUUPNT 00.9355 0 0798UUUGLS 0 0.9077 0 0718UUUPNT 0 0.8554 0 0526UUUSTLb 00.7797 0 0878UUUPNT 0 0.7784 0 0720UUUPNT 0 0.6402 0 0832UUUPNT 0 0.58590 0769UUUPNT 0 0.5093 0 1052UUUCLR 0 0.4904 0 0871UUUPNT 0 0.4257 00536UUUSTDr 0 0.4007 0 0493UUUSTDr 0 0.367 0 0493UUUSTD 0 0.3206 00753UUUPNT 0 0.168 0 0886UUUPNT 0 0.1593 0 0770UUUPNT 0 0.1142 00834UUURBR 0 0.0472 0 0876UUUPLS 0 0.0203 0 0524UUUPNT 0 0.018 00888UUUPNT 0 0.018 0 0724UUUPNT 0.9341 0.012 0.0307 0722UUUMBL 0 0.01030 1004UUUCNC 0.8766 0.0087 0.0203 1041UUUPNT 0 0.0058 0 0707UUUPNT 00.0035 0 0536UUUSTD 0 0.0031 0 0872UUUPNT 0 0.0031 0 0404UUUWOD 0 0.0030 0740UUUCNC 0 0.0011 0 0867UUURBR 0 0.001 0

Table 4 shows the three resulting P_(fa) values for each NEF material,sorted by combined P_(fa) value in decreasing order. It is clear fromTables 2-4 that the use of multi-angle signatures has given betteridentification results than either signature can give separately.

TABLE 4 P_(fa) for off- P_(fa) for near- P_(fa) for Candidate specularspecular combined Material signature signature signature 0724UUUPNT0.9341 0.012 0.0307 1004UUUCNC 0.8766 0.0087 0.0203 0122UUUALM 0.91 0 00400UUUCNC 0.8926 0 0 0603UUUCNC 0.8459 0 0 1312UUUALM 0.807 0 00898UUUFAB 0.6951 0 0 0971UUUCNC 0.6559 0 0 0893UUUFAB 0.5378 0 00588UUUCNC 0.5236 0 0 0605UUUSTO 0.5217 0 0 0838UUUPNT 0.5033 0 00713UUUCNC 0.4898 0 0 0014UUUALM 0.3983 0 0 0899UUUFAB 0.394 0 00671UUUCNC 0.3692 0 0 0593UUUCNC 0.2787 0 0 1074UUUFABa 0.2585 0 01039UUUCNC 0.2442 0 0 0864UUUCNC 0.2141 0 0 0822UUUPNT 0.2139 0 00490UUUASP 0.2083 0 0 0677UUUCNC 0.1892 0 0 0920UUUGRV 0.1613 0 00892UUUFAB 0.143 0 0 0915UUUCNC 0.132 0 0 0420UUUSTL 0.0623 0 00919UUUCNC 0.0607 0 0 1040UUUCNC 0.0563 0 0 0746UUUPNT 0.0445 0 0

Second, the performance prediction method and apparatus can be used bythe systems designer to determine the sensor calibration uncertainty andaerosol uncertainty needed to achieve a given performance level of amaterial identification method and apparatus. Assume that the materialidentification method performance level is formulated by a requiredprobability of false alarms (P_(fa-required)) at a given P_(d) value. Inthis section, the values P_(d)=95% and P_(fa-required)=5% will be usedfor the sake of example.

In order to simplify results, identification performance can bereformulated in terms of the “number of incorrect matches”, as follows.For each candidate material in the NEF, the PPT allows the designer topredict its actual probability of false alarms (P_(fa-actual)) at agiven P_(d). (Note that P_(fa-actual) will vary with sensor calibrationuncertainty and aerosol uncertainty.) In the event that P_(fa-actual)exceeds P_(fa-required), the target cannot be distinguished from thecandidate material, and the candidate material will then be deemed an“incorrect match”. The predicted performance example given above can bere-expressed in these terms as an example. FIG. 5 shows that when thetarget consists of NEF material 0835UUUPNT, the largest value over allcandidate materials of P_(fa-actual) was 3% if the sensor calibrationaccuracy is 4% and the aerosol uncertainty is 10%. Consequently, thereare no incorrect matches and the target can be distinguished from allcandidate materials.

The performance prediction method is then repeated for varying values ofsensor calibration uncertainty and aerosol uncertainty. The sensorcalibration uncertainty ranged from 0% to 10% in 2% increments, and theaerosol uncertainty ranged from 0% to 30% in 5% increments. The numbersof incorrect matches were determined, and for each sensor calibrationuncertainty value the results are displayed on a graph versus aerosoluncertainty, as shown in FIG. 5. This graph allows the system designerto trade off sensor calibration uncertainty and aerosol parameteruncertainty to achieve a given level of performance.

The performance prediction tool can also be repeated with differenttarget materials drawn from the NEF database. Table 5 shows results witha sensor radiometric calibration uncertainty value of 4%, but withaerosol uncertainty varying from 0 to 30% in 5% increments. The numbersof incorrect matches for the first 30 target materials vs. aerosoluncertainty are shown in Table 5.

TABLE 5 Results for other target materials using both images Aerosoluncertainty Material 0 5% 10% 15% 20% 25% 30% 0404UUUWOD 0 0 0 0 0 0 00430UUUPNT 0 0 0 0 0 0 0 0494UUUSTD 0 0 0 0 0 0 0 0607UUUPNT 0 0 0 0 0 00 0841UUUPNT 0 0 0 0 0 0 0 1144UUUSTL 0 0 0 0 0 0 0 1308UUUPNT 0 0 0 0 00 0 1323UUUPNT 0 0 0 0 0 0 0 0511UUUPNT 0 0 0 0 0 0 1 1302UUUPNT 0 0 0 00 0 1 1305UUUPLS 0 0 0 0 0 0 1 0407UUUPNT 0 0 0 0 0 1 1 0838UUUPNT 0 0 00 0 1 2 0122UUUALM 0 0 0 0 0 2 3 0874UUUCER 0 0 0 0 1 1 1 1053UUUMSC 0 00 0 1 1 2 0668UUUPNTb 0 0 0 0 1 2 3 0835UUUPNT 0 0 0 1 1 1 1 0879UUUMSC0 0 0 1 1 1 1 1074UUUFABb 0 0 0 1 1 1 2 1014UUUFIG 0 0 0 1 1 1 30408UUUPNT 0 0 0 1 1 2 2 0776UUUALM 0 0 0 1 2 2 2 0419UUUPNT 0 0 0 1 2 33 0997UUUPNT 0 0 0 1 2 4 6 0887UUUPNT 0 0 0 2 2 2 2 1019UUUFABc 0 0 1 11 1 1 0746UUUPNT 0 0 1 1 1 2 2 1074UUUFABa 0 0 1 1 2 2 2 0877UUUPLS 0 01 1 2 2 3

The results shown in Table 5 can provide performance information to thesystem designer and the consumer of the imagery. It is clear from thetable that this material identification method can successfullydistinguish many target materials from all other candidate materials inthe NEF database, given sufficiently accurate sensor and aerosolparameters. The table lists the level of aerosol uncertainty required toachieve this for each material. This is useful to the system designer insetting system requirements on aerosol knowledge. It is also useful tothe consumer of the imagery in determining whether a given set of datawill allow a specific target material to be identified.

The foregoing description is of exemplary and preferred embodimentsemploying at least in part certain teachings of the invention. Theinvention, as defined by the appended claims, is not limited to thedescribed embodiments. Alterations and modifications to the disclosedembodiments may be made without departing from the invention. Themeaning of the terms used in this specification, unless expressly statedotherwise, are intended to have ordinary and customary meaning, and arenot intended to be limited to the details of the illustrated structuresor the disclosed embodiments.

1. An implemented method for predicting a performance of a remote sensormaterial identification process under one or more given environmentalcondition and at least one uncertainty, the remote materialidentification process being used for automatically identifying apreselected target material within imagery acquired from one or moreremote sensors, the method comprising: setting at least oneenvironmental parameter representative of the one or more environmentalconditions and at least one uncertainty associated with at least one ofthe environmental parameters, or calibration of the one or more remotesensors; simulating, by a specially programmed computer processor, a“true” target spectral radiance at least one acquisition angle under theone or more environmental conditions, the target being made of apreselected material, the simulating being based on the at least oneenvironmental parameter, a type of sensor, and a previously measuredreflectance function for the preselected target material; performing, bythe specially programmed computer processor, the remote materialidentification process using the “true” target spectral radiance at theat least one acquisition angle, at least one environmental parameter,the material reflectance database, and at least one uncertainty todetermine an estimated target signature and uncertainty associated withthe estimated target signature, the material identification processfurther identifying the target material by comparing the estimatedtarget signature, a predicted spectral signature for each of at leastone candidate material at each of at least one acquisition angle, thepredicted spectral signature being determined by using BRDF for thecandidate material, the environmental parameter, and an uncertaintyassociated with the BRDF for the candidate material; and determining, bythe specially programmed computer processor, a probability of a falseidentification, using results of said remote material identificationprocess.
 2. The computer-implemented method of claim 1, furthercomprising: varying one or more of the at least one environmentalparameter and at least one uncertainty while iteratively repeating saidsetting, simulating, performing, and determining for the preselectedtarget material.
 3. The computer-implemented method of claim 2, furthercomprising: repeating said varying for each of a plurality ofpreselected target materials.
 4. The computer-implemented method ofclaim 3, further comprising: communicating results of at least one saiddetermining, said varying, or said repeating to a user.
 5. Thecomputer-implemented method of claim 4, wherein said user is at leastone of a designer of a material identification system or a consumer ofimage analysis results produced by the remote material identificationprocess.
 6. The computer-implemented method of claim 1, furthercomprising: receiving numerous types of input from a user via a userinterface of the specially programmed computer processor, including theat least one environmental parameter and the at least one uncertainty.7. The computer-implemented method of claim 1, further comprising:receiving a probability of detection from the user via the userinterface of the specially programmed computer processor, wherein saidperforming the remote material identification process includes utilizingthe probability of detection to generate the results of said performingthe remote material identification process.
 8. The computer-implementedmethod of claim 1, wherein the imagery is one or more of the followingtypes: (a) non-polarimetric reflective and/or emissive, multi-spectral(MS) or hyperspectral (HS); (b) polarimetric spectral reflective and/oremissive, MS or HS; or (c) synthetic aperture radar.
 9. Thecomputer-implemented method of claim 1, wherein said multi-anglematerial identification process is non-polarimetric reflective and/oremissive (MS), and said simulating involves determining at least twosets of atmospheric correction terms, including background dependentpath terms and aperture effective values.
 10. The computer-implementedmethod of claim 9, wherein the background dependent path terms aredetermined by: generating spectral background independent path termsfrom aerosol properties, the aerosol properties including absorption,asymmetry, and extinction; acquiring from a BRDF database directionalhemispherical spectral reflectance of a Lambertian background as afunction of wavelength; and utilizing the directional hemisphericalspectral reflectance to convert the background independent path terms tothe background dependent path terms.
 11. The computer-implemented methodof claim 9, wherein the aperture effective values are determined by:generating a BRDF atmosphere from aerosol properties, the aerosolproperties including absorption, asymmetry, and extinction; and usingthe BRDF atmosphere and the BRDF database to obtain aperture effectivevalues, including directional hemispherical reflectance of thebackground, directional hemispherical reflectance of the target,Lambertian-equivalent solar reflectance of the background, andLambertian-equivalent solar reflectance of the target.
 12. Thecomputer-implemented method of claim 9, further comprising: determiningbackground and target radiances using the background dependent pathterms and the aperture effective values.
 13. The computer-implementedmethod of claim 12, wherein said performing the remote materialidentification process includes determining an uncertainty in candidatesignatures attributable to BRDF measurement errors based on an errorcovariance matrix supplied by the BRDF database.
 14. Thecomputer-implemented method of claim 13, wherein said performing theremote material identification process includes determining achi-squared threshold for a given probability of detection.
 15. Thecomputer-implemented method of claim 14, wherein said determining theprobability of the misidentification includes observing the chi-squaredthreshold in evaluating a cumulative distribution of target reflectancesignatures and candidate reflectance signatures.
 16. An apparatus forpredicting a performance of a remote sensor material identificationprocess under one or more given environmental condition and at least oneuncertainty, the remote material identification process being used forautomatically identifying a preselected target material within imageryacquired from one or more remote sensors, the method comprising: meansfor setting at least one environmental parameter representative of theone or more environmental conditions and at least one uncertaintyassociated with at least one of the environmental parameter, orcalibration of the one or more remote sensors; means for simulating a“true” target spectral radiance of at least one acquisition angle underthe one or more environmental conditions, the target being made of apreselected material, the simulating being based on the at least oneenvironmental parameter, a type of sensor, and a previously measuredreflectance function for the preselected target material; means forperforming the remote material identification process using the “true”target spectral radiance at the at least one acquisition angle, the atleast one environmental parameter, the material reflectance database,and the at least one uncertainty to determine an estimated targetsignature and uncertainty associated with the estimated targetsignature, the material identification process further identifying thetarget material by comparing the estimated target signature, a predictedspectral signature for each of at least one candidate material at eachof the at least one acquisition angle, the predicted spectral signaturebeing determined by using BRDF for the candidate material, theenvironmental parameter, and an uncertainty associated with the BRDF forthe candidate material; and means for determining a probability of afalse identification, using results of said remote materialidentification process.
 17. The apparatus of claim 16, furthercomprising: means for varying one or more of the at least oneenvironmental parameter and the at least one uncertainty whileiteratively repeating said setting, simulating, performing, anddetermining for the preselected target material.
 18. The apparatus ofclaim 17, further comprising: means for repeating said varying for eachof a plurality of preselected target materials.
 19. The apparatus ofclaim 18, further comprising: means for communicating results of atleast one said determining, said varying, or said repeating to a user.20. The apparatus of claim 19, wherein said user is at least one ofdesigner of a material identification system or a consumer of imageanalysis results produced by the remote material identification process.21. The apparatus of claim 16, further comprising: means for receivingnumerous types of input from a user via a user interface of thespecially programmed computer processor, including the at least oneenvironmental parameter and the at least one uncertainty.
 22. Theapparatus of claim 16, further comprising: means for receiving aprobability of detection from the user via the user interface of thespecially programmed computer processor, wherein said performing theremote material identification process includes utilizing theprobability of detection to generate the results of said performing theremote material identification process.
 23. The apparatus of claim 16,wherein said imagery is one or more of the following types: (a)non-polarimetric reflective and/or emissive, multi-spectral (MS) orhyperspectral (HS); (b) polarimetric spectral reflective and/oremissive, MS or HS; or (c) synthetic aperture radar.
 24. The apparatusof claim 16, wherein said multi-angle material identification process isnon-polarimetric reflective and/or emissive (MS), and said means forsimulating determines at least two sets of atmospheric correction terms,including background dependent path terms and aperture effective values.25. The apparatus of claim 24, wherein said means for simulatingdetermines the background dependent path terms by: generating spectralbackground independent path terms from aerosol properties, the aerosolproperties including absorption, asymmetry, and extinction; acquiringfrom a BRDF database directional hemispherical spectral reflectance of aLambertian background as a function of wavelength; and utilizing thedirectional hemispherical spectral reflectance to convert the backgroundindependent path terms to the background dependent path terms.
 26. Theapparatus of claim 24, wherein said means for simulating determines theaperture effective values by: generating a BRDF atmosphere from aerosolproperties, the aerosol properties including absorption, asymmetry, andextinction; and passing the BRDF atmosphere to the BRDF database toobtain aperture effective values, including directional hemisphericalreflectance of the background, directional hemispherical reflectance ofthe target, Lambertian-equivalent solar reflectance of the background,and Lambertian-equivalent solar reflectance of the target.
 27. Theapparatus of claim 24, wherein said means for simulating determinesbackground and target radiances using the background dependent pathterms and the aperture effective values.
 28. The apparatus of claim 27,wherein said means for performing the remote material identificationprocess calculates an uncertainty in candidate signatures attributableto BRDF measurement errors based on an error covariance matrix suppliedby a BRDF database.
 29. The apparatus of claim 28, wherein said meansfor performing the remote material identification process determines achi-squared threshold for a given probability of detection.
 30. Theapparatus of claim 29, wherein said means for determining theprobability of the misidentification observes the chi-squared thresholdin evaluating a cumulative distribution of target reflectance signaturesand candidate reflectance signatures.
 31. A computer readable mediacarrying program instructions that, when executed by one or morecomputers, perform a method for predicting a performance of a remotesensor material identification process under one or more givenenvironmental condition and at least one uncertainty, the remotematerial identification process being used for automatically identifyinga preselected target material within imagery acquired from one or moreremote sensors, the method comprising: setting at least oneenvironmental parameter representative of the one or more environmentalconditions and at least one uncertainty associated with at least one ofthe environmental parameter, or calibration of the one or more remotesensors; simulating, by a specially programmed computer processor, a“true” target spectral radiance of at least one acquisition angle underthe one or more environmental conditions, the target being made of apreselected material, the simulating being based on the at least oneenvironmental parameter, a type of sensor, and a previously measuredreflectance function for the preselected target material; performing, bythe specially programmed computer processor, the remote materialidentification process using the “true” target spectral radiance at theat least one acquisition angle, the at least one environmentalparameter, the material reflectance database, and the at least oneuncertainty to determine an estimated target signature and uncertaintyassociated with the estimated target signature, the materialidentification process further identifying the target material bycomparing the estimated target signature, a predicted spectral signaturefor each of at least one candidate material at each of the at least oneacquisition angle, the predicted spectral signature being determined byusing BRDF for the candidate material, the environmental parameter, andan uncertainty associated with the BRDF for the candidate material; anddetermining, by the specially programmed computer processor, aprobability of a false identification, using results of said remotematerial identification process.
 32. The computer readable media ofclaim 31, wherein the method further comprises: varying one or more ofthe at least one environmental parameter and the at least oneuncertainty while iteratively repeating said setting, simulating,performing, and determining for the preselected target material.
 33. Thecomputer readable media of claim 32, wherein the method furthercomprises: repeating said varying for each of a plurality of preselectedtarget materials.
 34. The computer readable media of claim 33, whereinthe method further comprises: communicating results of at least one saiddetermining, said varying, or said repeating to a user.
 35. The computerreadable media of claim 34, wherein said user is at least one ofdesigner of a material identification system or a consumer of imageanalysis results produced by the remote material identification process.36. The computer readable media of claim 31, wherein the method furthercomprises: receiving numerous types of input from a user via a userinterface of the specially programmed computer processor, including theat least one environmental parameter and the at least one uncertainty.37. The computer readable media of claim 31, wherein the method furthercomprises: receiving a probability of detection from the user via theuser interface of the specially programmed computer processor, whereinsaid performing the remote material identification process includesutilizing the probability of detection to generate the results of saidperforming the remote material identification process.
 38. The computerreadable media of claim 31, wherein the imagery is one or more of thefollowing types: (a) non-polarimetric reflective and/or emissive,multi-spectral (MS) or hyperspectral (HS); (b) polarimetric spectralreflective and/or emissive, MS or HS; or (c) synthetic aperture radar.39. The computer readable media of claim 31, wherein said multi-anglematerial identification process is non-polarimetric reflective and/oremissive (MS), and said simulating involves determining at least twosets of atmospheric correction terms, including background dependentpath terms and aperture effective values.
 40. The computer readablemedia of claim 39, wherein the background dependent path terms aredetermined by: generating spectral background independent path termsfrom aerosol properties, the aerosol properties including absorption,asymmetry, and extinction; acquiring from a BRDF database directionalhemispherical spectral reflectance of a Lambertian background as afunction of wavelength; and utilizing the directional hemisphericalspectral reflectance to convert the background independent path terms tothe background dependent path terms.
 41. The computer readable media ofclaim 39, wherein the aperture effective values are determined by:generating a BRDF atmosphere from aerosol properties, the aerosolproperties including absorption, asymmetry, and extinction; and usingthe BRDF atmosphere to the BRDF database to obtain aperture effectivevalues, including directional hemispherical reflectance of thebackground, directional hemispherical reflectance of the target,Lambertian-equivalent solar reflectance of the background, andLambertian-equivalent solar reflectance of the target.
 42. The computerreadable media of claim 39 further comprising: determining backgroundand target radiances using the background dependent path terms and theaperture effective values.
 43. The computer readable media of claim 32,wherein said performing the remote material identification processincludes determining an uncertainty in candidate signatures attributableto BRDF measurement errors based on an error covariance matrix suppliedby a BRDF database.
 44. The computer readable media of claim 33, whereinsaid performing the remote material identification process includesdetermining a chi-squared threshold for a given probability ofdetection.
 45. The computer readable media of claim 34, wherein saiddetermining the probability of the misidentification includes observingthe chi-squared threshold in evaluating a cumulative distribution oftarget reflectance signatures and candidate reflectance signatures.